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On the Numerical Solution of Finite-Dimensional Variational Inequalities by an Interior Point Method

  • Chapter
Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 58))

Abstract

In this paper we give an Inexact Interior Point method to solve finitedimensional variational inequality problems for monotone functions and polyhedral sets. At each iteration the linear system that determines the search direction is solved inexactly, by using a linear iterative solver with an ad hoc stopping criterion. We discuss algorithmic issues concerning the solution of several subproblems arising in the formulation of the method, including: form of the linear systems to be solved, choice of the accuracy in the solution of these systems, strategy for satisfying centering and descent conditions. Not surprisingly, all these choices can affect the actual performance of the method, both in terms of reliability and efficiency. We describe the practical and theoretical considerations behind the decisions included in our implementation. Results of the numerical experimentation on several well known test problems are given. They confirm the effectiveness of the proposed algorithm.

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Author information

Authors and Affiliations

  1. Dipartimento di Energetica “S. Stecco”, Università di Firenze, Via C.Lombroso 6/17, 50134, Firenze, Italia

    Stefania Bellavia & Maria Grazia Gasparo

Authors
  1. Stefania Bellavia
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  2. Maria Grazia Gasparo
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Editor information

Editors and Affiliations

  1. University of Pisa, Italy

    Franco Giannessi

  2. University of Catania, Italy

    Antonino Maugeri

  3. University of Florida, USA

    Panos M. Pardalos

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© 2001 Kluwer Academic Publishers

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Bellavia, S., Gasparo, M.G. (2001). On the Numerical Solution of Finite-Dimensional Variational Inequalities by an Interior Point Method. In: Giannessi, F., Maugeri, A., Pardalos, P.M. (eds) Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications, vol 58. Springer, Boston, MA. https://doi.org/10.1007/0-306-48026-3_1

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  • DOI: https://doi.org/10.1007/0-306-48026-3_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-0161-1

  • Online ISBN: 978-0-306-48026-3

  • eBook Packages: Springer Book Archive

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